The polished back-to-the-basket big man, or the versatile two-way dynamo with arguably the higher upside? The New Jersey kid who nearly led Kentucky to a perfect season, or the Chicagoan who won a national title with Duke?

The Timberwolves have their choice of potentially dominant big men — Karl-Anthony Towns or Jahlil Okafor — when the NBA draft kicks off Thursday night, a choice few have had over the years.

“We’re going to try to make an impact right away,” Okafor said Wednesday at the Westin Hotel in Midtown.

The NBA has seen changes recently in the effectiveness of pounding the ball in the paint, with 3-point shooting teams such as the Warriors and Spurs winning the last two NBA titles. But Towns and Okafor could signal a change — at least for their future teams.

“You still need the big man to do the dirty work, and also change up the philosophy of the defense,” Towns said. “Having a player play with his back to the basket changes up the game, because it changes up the way you look at the offense and the way you have to play defense.”

Towns, a 6-foot-11 Piscataway, N.J. native with perimeter skills, is the likely top pick. Because of Kentucky’s ridiculous depth, he spent his entire freshman year in the paint. He performed quite well in John Calipari’s platoon system, leading the Wildcats to the Final Four with a memorable 25-point performance in the Elite Eight. He showed versatility in workouts, displaying a sweet stroke from beyond the 3-point arc most players his size only dream of.

“My dad always told me, ‘Karl, if you work hard, and work hard to make sure you’re as versatile as possible, the coach has no choice but to put you in the game,’” Towns said.

Towns said he is excited about the potential of the Timberwolves, assuming he is their pick. He would like to learn how to become a champion from veteran Kevin Garnett and join their young core of gifted athletes.

“Not only is Andrew Wiggins explosive, but they also have Ricky Rubio, Zach LaVine. You’re talking about really explosive players,” Towns said. “That team is going to be really good.”

Okafor, a 6-10 big man with advanced footwork and post moves, was predicted to be the top pick of this year’s draft since his junior year of high school. He helped Duke win the national title, averaging 17.3 points per game, but unlike Towns, his rebounding and defense have been questioned. When asked about that criticism, he initially gave a diplomatic answer.

“I don’t think anything of it,” he said. “I’m just 19 years old, trying to get better every day.”

But Okafor did add, when asked if he should be the No. 1 pick: “I’m a winner — I’ve always been a winner. … I’m very confident. I don’t have any doubts. I feel confident I can make an impact in the NBA [right away]. I can dominate the way I am.”

If Okafor goes to the Lakers No. 2, as many expect, he would find himself on the same team as Kobe Bryant. He wouldn’t mind the challenge of teaming with the demanding future Hall of Famer.

“Nothing intimidates me,” he said. “Everything he does, he wants to win, and so do I. That’s something I admire.

“They have a great reputation for big men coming to them, dominating, and the results have been NBA championships. I know if I was fortunate to go there I would have big shoes to fill. It’s a lot of expectations going there, but I’m excited about it if I did end up going there.”

Whatever happens Thursday night, Okafor and Towns will be forever connected and compared for years to come. Right now, they’re just trying to enjoy the moment. They’re close friends, having met on a recruiting visit to Duke years ago, a visit that went so well they talked about attending school together. They remained in contact and kept in touch through this hectic draft process.

“We’re going through the exact same thing,” Okafor said. “We’re all excited, our families are both excited, and we’re both ready for Thursday to go to our new city.”